What license do you need to drive snowplow truck?

That depends on exactly what you're driving. A pickup truck with a snowplow mounted on the front doesn't require a CDL. A single axle dump truck weighing under 26,000 lbs doesn't, either. The moment that vehicle weighs over 26,000 lbs., or if you're driving a tandem/tri-axle/quad axle/etc. dump truck with a plow, then you need a Class B CDL. If, at any point, you're driving a combination (of truck and trailer) with a Gross Vehicle Weight Rating of over 26,000 lbs, and the vehicle in tow is rated at over 10,000 lbs, then you need a Class A CDL.